Locally induced, magnetic order on the surface of a topological insulator nanowire could enable room-temperature topological quantum devices. Here we report on the realization of selective magnetic control over topological surface states on a single facet of a rectangular Bi2Te3 nanowire via a magnetic insulating Fe3O4 substrate. Low-temperature magnetotransport studies provide evidence for local time-reversal symmetry breaking and for enhanced gapping of the interfacial 1D energy spectrum by perpendicular magnetic-field components, leaving the remaining nanowire facets unaffected. Our results open up great opportunities for development of dissipation-less electronics and spintronics.